Finite Group Databasebeta

← Group #243191

Character table — Group #243191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444444444442244888888888888888888888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111-1-11111-1-1
χ121111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-111-1-1-1-111
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-11-111-1-1-1-111-1-111
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-11-11-1-11111-1-111-1-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-11-1-1-11111-1-1-1-111
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-1111-1-1-1-11111-1-1
χ17222222222222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-22222-2-2-2-222222222-2-2-2-2-2-20000000000000000000000000000000022-2-2000000000000
χ2222222222-2-22222-2-2-2-222222222-2-2-2-2-2-200000000000000000000000000000000-2-222000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222000000000000000000000000000000000000000000002i−2i−2i2i
χ2622222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22200000000000000000000000000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-22222-2-2-2-22222-2-222-2-2000000000000000000000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-22222-2-222-2-200000000000000000000000000000000-222-2000000000000
χ292222-2-2-2-22222-2-222-2-222-2-222-2-2-2-22-22-200000000000000000000000022-2-222-2-20000000000000000
χ302222-2-2-2-22222-2-222-2-222-2-222-2-2-2-22-22-2000000000000000000000000-2-222-2-2220000000000000000
χ312222-2-2-2-22222-2-222-2-2-2-222-2-222-2-2-22-22000000000000000022-2-222-2-2000000000000000000000000
χ322222-2-2-2-22222-2-222-2-2-2-222-2-222-2-2-22-220000000000000000-2-222-2-222000000000000000000000000
χ332222-2-2-2-222-2-222-2-22222-2-2-2-222-2-22-2-22000000000000000022-2-2-2-222000000000000000000000000
χ342222-2-2-2-222-2-222-2-22222-2-2-2-222-2-22-2-220000000000000000-2-22222-2-2000000000000000000000000
χ352222-2-2-2-222-2-222-2-222-2-22222-2-2-2-2-222-200000000000000000000000022-2-2-2-2220000000000000000
χ362222-2-2-2-222-2-222-2-222-2-22222-2-2-2-2-222-2000000000000000000000000-2-22222-2-20000000000000000
χ372222-2-2-2-2-2-222-2-2-2-22222-2-222-2-222-22-2200000000000000000000000000000000000000002i−2i2i−2i0000
χ382222-2-2-2-2-2-222-2-2-2-22222-2-222-2-222-22-220000000000000000000000000000000000000000−2i2i−2i2i0000
χ392222-2-2-2-2-2-222-2-2-2-222-2-222-2-222222-22-20000000000000000000000000000000000002i−2i2i−2i00000000
χ402222-2-2-2-2-2-222-2-2-2-222-2-222-2-222222-22-2000000000000000000000000000000000000−2i2i−2i2i00000000
χ412222-2-2-2-2-2-2-2-22222-2-222-2-2-2-22222-222-20000000000000000000000000000000000002i−2i−2i2i00000000
χ422222-2-2-2-2-2-2-2-22222-2-222-2-2-2-22222-222-2000000000000000000000000000000000000−2i2i2i−2i00000000
χ432222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2222-2-2200000000000000000000000000000000000000002i−2i−2i2i0000
χ442222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2222-2-220000000000000000000000000000000000000000−2i2i2i−2i0000
χ4522-2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2000000002i2i−2i−2i000022-2-2i2−i2i2−i22−22−22−22−2i2−i2i2−i20000000000000000
χ4622-2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2000000002i2i−2i−2i000022-2-2−i2i2−i2i2−22−22−22−22−i2i2−i2i20000000000000000
χ4722-2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-200000000−2i−2i2i2i0000-2-222i2−i2i2−i22−22−2−22−22−i2i2−i2i20000000000000000
χ4822-2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-200000000−2i−2i2i2i0000-2-222−i2i2−i2i2−22−222−22−2i2−i2i2−i20000000000000000
χ4922-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2000000002i2i−2i−2i0000-2-222i2−i2i2−i2−22−222−22−2−i2i2−i2i20000000000000000
χ5022-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2000000002i2i−2i−2i0000-2-222−i2i2−i2i22−22−2−22−22i2−i2i2−i20000000000000000
χ5122-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-200000000−2i−2i2i2i000022-2-2i2−i2i2−i2−22−22−22−22i2−i2i2−i20000000000000000
χ5222-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-200000000−2i−2i2i2i000022-2-2−i2i2−i2i22−22−22−22−2−i2i2−i2i20000000000000000
χ5322-2-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000-2200002i2i−2i−2i000022-2-20000i2−i2−i2i22−2−222−2−22i2−i2−i2i20000000000000000
χ5422-2-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000-2200002i2i−2i−2i000022-2-20000−i2i2i2−i2−222−2−222−2−i2i2i2−i20000000000000000
χ5522-2-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000-220000−2i−2i2i2i0000-2-2220000i2−i2−i2i22−2−22−222−2−i2i2i2−i20000000000000000
χ5622-2-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000-220000−2i−2i2i2i0000-2-2220000−i2i2i2−i2−222−22−2−22i2−i2−i2i20000000000000000
χ5722-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000-2200002i2i−2i−2i0000-2-2220000i2−i2−i2i2−222−22−2−22−i2i2i2−i20000000000000000
χ5822-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000-2200002i2i−2i−2i0000-2-2220000−i2i2i2−i22−2−22−222−2i2−i2−i2i20000000000000000
χ5922-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000-220000−2i−2i2i2i000022-2-20000i2−i2−i2i2−222−2−222−2i2−i2−i2i20000000000000000
χ6022-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000-220000−2i−2i2i2i000022-2-20000−i2i2i2−i22−2−222−2−22−i2i2i2−i20000000000000000
χ6144-4-44-44-4-444i−4i4i−4i−4i4i−4i4i00000000-440000000000000000000000000000000000000000000000000000
χ6244-4-44-44-4-44−4i4i−4i4i4i−4i4i−4i00000000-440000000000000000000000000000000000000000000000000000
χ6344-4-4-44-44-444i−4i−4i4i−4i4i4i−4i000000004-40000000000000000000000000000000000000000000000000000
χ6444-4-4-44-44-44−4i4i4i−4i4i−4i−4i4i000000004-40000000000000000000000000000000000000000000000000000
χ654-44-444-4-4000000000000004-44-40000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ664-44-444-4-4000000000000004-44-400000000000000−2222−2222−2222−222200000000000000000000000000000000
χ674-44-444-4-400000000000000-44-440000000000000022−2222−22−2222−222200000000000000000000000000000000
χ684-44-444-4-400000000000000-44-4400000000000000−2222−222222−2222−2200000000000000000000000000000000
χ694-44-4-4-444000000000000004-4-4400000022−2222−2222−2222−220000000000000000000000000000000000000000
χ704-44-4-4-444000000000000004-4-44000000−2222−2222−2222−22220000000000000000000000000000000000000000
χ714-44-4-4-44400000000000000-444-400000022−2222−22−2222−22220000000000000000000000000000000000000000
χ724-44-4-4-44400000000000000-444-4000000−2222−222222−2222−220000000000000000000000000000000000000000
χ734-4-444-4-4400000000004i−4i4i−4i00000000002i2−2i2−2i22i20000000022−22−222200000000000000000000000000000000
χ744-4-444-4-4400000000004i−4i4i−4i0000000000−2i22i22i2−2i200000000−222222−2200000000000000000000000000000000
χ754-4-444-4-440000000000−4i4i−4i4i00000000002i2−2i2−2i22i200000000−222222−2200000000000000000000000000000000
χ764-4-444-4-440000000000−4i4i−4i4i0000000000−2i22i22i2−2i20000000022−22−222200000000000000000000000000000000
χ774-4-44-444-400000000004i−4i−4i4i000000000000002i2−2i2−2i22i2−222222−22000000000000000000000000000000000000
χ784-4-44-444-400000000004i−4i−4i4i00000000000000−2i22i22i2−2i222−22−2222000000000000000000000000000000000000
χ794-4-44-444-40000000000−4i4i4i−4i000000000000002i2−2i2−2i22i222−22−2222000000000000000000000000000000000000
χ804-4-44-444-40000000000−4i4i4i−4i00000000000000−2i22i22i2−2i2−222222−22000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).